Tool
Spur Gear Calculator
Spur-gear geometry from module or diametral pitch — pitch / base / outside / root diameters, center distance, gear ratio, output speed and torque.
Inputs
Pitch system
EquivalentDP ≈ 12.70
Pinion (N₁)
Pitch diameter (d)40.000 mm1.5748 in
Outside diameter44.000 mm1.7323 in
Root diameter35.000 mm1.3780 in
Base diameter37.588 mm1.4798 in
Addendum2.000 mm0.0787 in
Dedendum2.500 mm0.0984 in
Whole depth4.500 mm0.1772 in
Circular pitch6.283 mm0.2474 in
Tooth thickness (at PCD)3.142 mm0.1237 in
Gear (N₂)
Pitch diameter (D)120.000 mm4.7244 in
Outside diameter124.000 mm4.8819 in
Root diameter115.000 mm4.5276 in
Base diameter112.763 mm4.4395 in
Addendum2.000 mm0.0787 in
Dedendum2.500 mm0.0984 in
Whole depth4.500 mm0.1772 in
Circular pitch6.283 mm0.2474 in
Tooth thickness (at PCD)3.142 mm0.1237 in
Mesh
Gear ratio (N₂/N₁)3.000 : 1
Center distance80.000 mm3.1496 in
Speed
Input RPM1750
Output RPM583.3
Torque (lossless / with η)
Input torque6.00 lbf·ft8.14 N·m
Output torque (× η)17.47 lbf·ft23.68 N·m
Notes
- Standard full-depth involute teeth — addendum = m, dedendum = 1.25 m, whole depth = 2.25 m.
- Module (mm) and Diametral Pitch (1/in) are reciprocals through 25.4: m = 25.4 / DP.
- Most industrial spur gears use a 20° pressure angle (some legacy 14.5° or modern 25°).
- Avoid undercutting — minimum pinion teeth ≈ 17 at 20° pressure angle.
- Gear ratio > 6:1 in a single stage gets large & inefficient; stage if needed.
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